Решите систему уравнений: x²+2y=7; y²-6x=-17.

\[\left\{ \begin{matrix} x^{2} + 2y = 7\ \ \ \ \ \ \ \ \ \ \ \ (1) \\ y^{2} - 6x = - 17\ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} (x - 3)^{2} + (y + 1)^{2} = 0 \\ x^{2} + 2y = 7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \ \]

\[3^{2} + 2 \cdot ( - 1) = 7\]

\[9 - 2 = 7\]

\[7 = 7 \Longrightarrow (3;\ - 1) \Longrightarrow решение.\]

\[Ответ:(3;\ - 1).\]